FIG. 1A depicts a portion of a prior art reflective (i.e. front-lit) image display 10 in which total internal reflection (TIR) is electrophoretically modulated as described in U.S. Pat. Nos. 6,885,496 and 6,891,658. Display 10 includes a transparent outward sheet 12 formed by partially embedding a large plurality of high refractive index (e.g. η1>˜1.90) transparent spherical or approximately spherical beads 14 in the inward surface of a high refractive index (e.g. η2>˜1.75) polymeric material 16 having a flat outward viewing surface 17 which viewer V observes through an angular range of viewing directions Y. The “inward” and “outward” directions are indicated by double-headed arrow Z. Beads 14 are packed closely together to form an inwardly projecting monolayer 18 having a thickness approximately equal to the diameter of one of beads 14. Ideally, each one of beads 14 touches all of the beads immediately adjacent to that one bead. Minimal interstitial gaps (ideally, no gaps) remain between adjacent beads.
An electrophoresis medium 20 is maintained adjacent the portions of beads 14 which protrude inwardly from material 16 by containment of medium 20 within a reservoir 22 defined by lower sheet 24. An inert, low refractive index (i.e. less than about 1.35), low viscosity, electrically insulating liquid such as Fluorinert™ perfluorinated hydrocarbon liquid (η3˜1.27) available from 3M, St. Paul, Minn. is a suitable electrophoresis medium. Other liquids, or water can also be used as electrophoresis medium 20. A bead:liquid TIR interface is thus formed. Medium 20 contains a finely dispersed suspension of light scattering and/or absorptive particles 26 such as pigments, dyed or otherwise scattering/absorptive silica or latex particles, etc. Sheet 24's optical characteristics are relatively unimportant: sheet 24 need only form a reservoir for containment of electrophoresis medium 20 and particles 26, and serve as a support for backplane electrode 48.
As is well known, the TIR interface between two media having different refractive indices is characterized by a critical angle θc. Light rays incident upon the interface at angles less than θc are transmitted through the interface. Light rays incident upon the interface at angles greater than θc undergo TIR at the interface. A small critical angle is preferred at the TIR interface since this affords a large range of angles over which TIR may occur.
In the absence of electrophoretic activity, as is illustrated to the right of dashed line 28 in FIG. 1A, a substantial fraction of the light rays passing through sheet 12 and beads 14 undergoes TIR at the inward side of beads 14. For example, incident light rays 30, 32 are refracted through material 16 and beads 14. The rays undergo TIR two or more times at the bead:liquid TIR interface, as indicated at points 34, 36 in the case of ray 30; and indicated at points 38, 40 in the case of ray 32. The totally internally reflected rays are then refracted back through beads 14 and material 16 and emerge as rays 42, 44 respectively, achieving a “white” appearance in each reflection region or pixel.
A voltage can be applied across medium 20 via electrodes 46, 48 (shown as dashed lines) which can for example be applied by vapour-deposition to the inwardly protruding surface portion of beads 14 and to the outward surface of sheet 24. Electrode 46 is transparent and substantially thin to minimize its interference with light rays at the bead:liquid TIR interface. Backplane electrode 48 need not be transparent. If electrophoresis medium 20 is activated by actuating voltage source 50 to apply a voltage between electrodes 46, 48 as illustrated to the left of dashed line 28, suspended particles 26 are electrophoretically moved into the region where the evanescent wave is relatively intense (i.e. within 0.25 micron of the inward surfaces of inwardly protruding beads 14, or closer). When electrophoretically moved as aforesaid, particles 26 scatter or absorb light, thus frustrating TIR by modifying the imaginary and possibly the real component of the effective refractive index at the bead:liquid TIR interface. This is illustrated by light rays 52, 54 which are scattered and/or absorbed as they strike particles 26 inside the thin (˜0.5 μm) evanescent wave region at the bead:liquid TIR interface, as indicated at 56, 58 respectively, thus achieving a “dark” appearance in each TIR-frustrated non-reflective absorption region or pixel. Particles 26 need only be moved outside the thin evanescent wave region, by suitably actuating voltage source 50, in order to restore the TIR capability of the bead:liquid TIR interface and convert each “dark” non-reflective absorption region or pixel to a “white” reflection region or pixel.
As described above, the net optical characteristics of outward sheet 12 can be controlled by controlling the voltage applied across medium 20 via electrodes 46, 48. The electrodes can be segmented to control the electrophoretic activation of medium 20 across separate regions or pixels of sheet 12, thus forming an image.
FIG. 2 depicts, in enlarged cross-section, an inward hemispherical or “hemi-bead” portion 60 of one of spherical beads 14. Hemi-bead 60 has a normalized radius r=1 and a refractive index η1. A light ray 62 perpendicularly incident (through material 16) on hemi-bead 60 at a radial distance α from hemi-bead 60's centre C encounters the inward surface of hemi-bead 60 at an angle θ1 relative to radial axis 66. For purposes of this theoretically ideal discussion, it is assumed that material 16 has the same refractive index as hemi-bead 60 (i.e. η1=η2), so ray 62 passes from material 16 into hemi-bead 60 without refraction. Ray 62 is refracted at the inward surface of hemi-bead 60 and passes into electrophoretic medium 20 as ray 64 at an angle θ2 relative to radial axis 66.
Now consider incident light ray 68 which is perpendicularly incident (through material 16) on hemi-bead 60 at a distance
      a    c    =            η      3              η      1      from hemi-bead 60's centre C. Ray 68 encounters the inward surface of hemi-bead 60 at the critical angle θc (relative to radial axis 70), the minimum required angle for TIR to occur. Ray 68 is accordingly totally internally reflected, as ray 72, which again encounters the inward surface of hemi-bead 60 at the critical angle θc. Ray 72 is accordingly totally internally reflected, as ray 74, which also encounters the inward surface of hemi-bead 60 at the critical angle θc. Ray 74 is accordingly totally internally reflected, as ray 76, which passes perpendicularly through hemi-bead 60 into the embedded portion of bead 14 and into material 16. Ray 68 is thus reflected back as ray 76 in a direction approximately opposite that of incident ray 68.
All light rays which are incident on hemi-bead 60 at distances α≧αc from hemi-bead 60's centre C are reflected back (but not exactly retro-reflected) toward the light source; which means that the reflection is enhanced when the light source is overhead and slightly behind the viewer, and that the reflected light has a diffuse characteristic giving it a white appearance, which is desirable in reflective display applications. FIGS. 3A, 3B and 3C depict three of hemi-bead 60's reflection modes. These and other modes coexist, but it is useful to discuss each mode separately.
In FIG. 3A, light rays incident within a range of distances αc<α≦α1 undergo TIR twice (the 2-TIR mode) and the reflected rays diverge within a comparatively wide arc φ1 centered on a direction opposite to the direction of the incident light rays. In FIG. 3B, light rays incident within a range of distances α1<α≦α2 undergo TIR three times (the 3-TIR mode) and the reflected rays diverge within a narrower arc φ2<φ1 which is again centered on a direction opposite to the direction of the incident light rays. In FIG. 3C, light rays incident within a range of distances α2<α≦α3 undergo TIR four times (the 4-TIR mode) and the reflected rays diverge within a still narrower arc φ3<φ2 also centered on a direction opposite to the direction of the incident light rays. Hemi-bead 60 thus has a “semi-retro-reflective,” partially diffuse reflection characteristic, causing display 10 to have a diffuse appearance akin to that of paper.
Display 10 has relatively high apparent brightness, comparable to that of paper, when the dominant source of illumination is behind the viewer, within a small angular range. This is illustrated in FIG. 1B which depicts the wide angular range α over which viewer V is able to view display 10, and the angle β which is the angular deviation of illumination source S relative to the location of viewer V. Display's 10's high apparent brightness is maintained as long as β is not too large. At normal incidence, the reflectance R of hemi-bead 60 (i.e. the fraction of light rays incident on hemi-bead 60 that reflect by TIR) is given by equation (1):
                    R        =                  1          -                                    (                                                η                  3                                                  η                  1                                            )                        2                                              (        1        )            where η1 is the refractive index of hemi-bead 60 and η3 is the refractive index of the medium adjacent the surface of hemi-bead 60 at which TIR occurs. Thus, if hemi-bead 60 is formed of a lower refractive index material such as polycarbonate (η1˜1.59) and if the adjacent medium is Fluorinert (η3˜1.27), a reflectance R of about 36% is attained, whereas if hemi-bead 60 is formed of a high refractive index nano-composite material (η1˜1.92) a reflectance R of about 56% is attained. When illumination source S (FIG. 1B) is positioned behind viewer V's head, the apparent brightness of display 10 is further enhanced by the aforementioned semi-retro-reflective characteristic.
As shown in FIGS. 4A-4G, hemi-bead 60's reflectance is maintained over a broad range of incidence angles, thus enhancing display 10's wide angular viewing characteristic and its apparent brightness. For example, FIG. 4A shows hemi-bead 60 as seen from perpendicular incidence—that is, from an incidence angle offset 0° from the perpendicular. In this case, the portion 80 of hemi-bead 60 for which α≧αc appears as an annulus. The annulus is depicted as white, corresponding to the fact that this is the region of hemi-bead 60 which reflects incident light rays by TIR, as aforesaid. The annulus surrounds a circular region 82 which is depicted as dark, corresponding to the fact that this is the non-reflective region of hemi-bead 60 within which incident rays are absorbed and do not undergo TIR. FIGS. 4B-4G show hemi-bead 60 as seen from incident angles which are respectively offset 15°, 30°, 45°, 60°, 75° and 90° from the perpendicular. Comparison of FIGS. 4B-4G with FIG. 4A reveals that the observed area of reflective portion 80 of hemi-bead 60 for which α≧αc decreases only gradually as the incidence angle increases. Even at near glancing incidence angles (e.g. FIG. 4F) an observer will still see a substantial part of reflective portion 80, thus giving display 10 a wide angular viewing range over which high apparent brightness is maintained.
An estimate of the reflectance of an array of hemispheres corresponding to the inward “hemi-bead” portions of each one of spherical beads 14 depicted in FIG. 1A can be obtained by multiplying the reflectance of an individual hemi-bead by the hemi-beads' packing efficiency coefficient f. Calculation of the packing efficiency coefficient f of a closely packed structure involves application of straightforward geometry techniques which are well known to persons skilled in the art. The hexagonal closest packed (HCP) structure depicted in FIG. 5 yields a packing efficiency f∝π/(6·tan 30°)˜90.7% assuming beads 14 are of uniform size.
Although the HCP structure yields the highest packing density for hemispheres, it is not necessary to pack the hemi-beads in a regular arrangement, nor is it necessary that the hemi-beads be of uniform size. A random distribution of non-uniform size hemi-beads having diameters within a range of about 1-50 μm has a packing density of approximately 80%, and has an optical appearance substantially similar to that of an HCP arrangement of uniform size hemi-beads. For some reflective display applications, such a randomly distributed arrangement may be more practical to manufacture, and for this reason, somewhat reduced reflectance due to less dense packing may be acceptable. However, for simplicity, the following description focuses on the FIG. 5 HCP arrangement of uniform size hemi-beads, and assumes the use of materials which yield a refractive index ratio η1/η3=1.5. These factors are not to be considered as limiting the scope of this disclosure.
As previously explained in relation to FIG. 2, a substantial portion of light rays which are perpendicularly incident on the flat outward face of hemi-bead 60 at distances α<αc from hemi-bead 60's centre C do not undergo TIR and are therefore not reflected by hemi-bead 60. Instead, a substantial portion of such light rays are scattered and/or absorbed by prior art display 10, yielding a dark non-reflective circular region 82 (FIGS. 4A-4G) on hemi-bead 60. FIG. 5 depicts a plurality of these dark non-reflective regions 82, each of which is surrounded by a reflective annular region 80, as previously explained.
Hemi-bead 60's average surface reflectance, R, is determined by the ratio of the area of reflective annulus 80 to the total area comprising reflective annulus 80 and dark circular region 82. That ratio is in turn determined by the ratio of the refractive index, η1, of hemi-bead 60 to the refractive index, η3, of the medium adjacent the surface of hemi-bead 60 at which TIR occurs, in accordance with Equation (1). It is thus apparent that the average surface reflectance, R, increases with the ratio of the refractive index η1, of hemi-bead 60 to that of the adjacent medium η3. For example, the average surface reflectance, R, of a hemispherical water drop (η1˜1.33) in air (η3˜1.0) is about 43%; the average surface reflectance, R, of a glass hemisphere (η1˜1.5) in air is about 55%; and the average surface reflectance, R, of a diamond hemisphere (η1˜2.4) in air exceeds 82%.
Although it may be convenient to fabricate display 10 using spherically (or hemispherically) shaped beads as aforesaid, even if spherical (or hemispherical) beads 14 are packed together as closely as possible within monolayer 18 (FIG. 1A), interstitial gaps 84 (FIG. 5) unavoidably remain between adjacent beads. Light rays incident upon any of gaps 84 are “lost” in the sense that they pass directly into electrophoretic medium 20, producing undesirable dark spots on viewing surface 17. While these spots are invisibly small, and therefore do not detract from display 10's appearance, they do detract from viewing surface 17's net average surface reflectance, R.
The above-described “semi-retro-reflective” characteristic is important in a reflective display because, under typical viewing conditions where light source S is located above and behind viewer V, a substantial fraction of the reflected light is returned toward viewer V. This results in an apparent reflectance which exceeds the value
  R  =      1    -                  (                              η            3                                η            1                          )            2      by a “semi-retro-reflective enhancement factor” of about 1.5 (see “A High Reflectance, Wide Viewing Angle Reflective Display Using Total Internal Reflection in Micro-Hemispheres,” Mossman, M. A. et al., Society for Information Display, 23rd International Display Research Conference, pages 233-236, Sep. 15-18, 2003, Phoenix, Ariz.). For example, in a system where the refractive index ratio η1/η3=1.5, the average surface reflectance, R, of 55% determined in accordance with Equation (1) is enhanced to approximately 85% under the semi-retro-reflective viewing conditions described above.
Individual hemi-beads 60 can be invisibly small, within the range of 2-50 μm in diameter, and as shown in FIG. 5 they can be packed into an array to create a display surface that appears highly reflective due to the large plurality of tiny, adjacent, reflective annular regions 80. In these regions 80, where TIR can occur, particles 26 (FIG. 1A) do not impede the reflection of incident light when they are not in contact with the inward, hemispherical portions of beads 14. However, in regions 82 and 84, where TIR does not occur, particles 26 may absorb incident light rays—even if particles 26 are moved outside the evanescent wave region so that they are not in optical contact with the inward, hemispherical portions of beads 14. The refractive index ratio η1/η3 can be increased in order to increase the size of each reflective annular region 80 and thus reduce such absorption losses. Non-reflective regions 82, 84 cumulatively reduce display 10's overall surface reflectance, R. Since display 10 is a reflective display, it is clearly desirable to minimize such reduction.
Disregarding the aforementioned semi-retro-reflective enhancement factor, a system having a refractive index ratio η1/η3=1.5 has an average surface reflectance, R, of 55%, as previously explained. Given the HCP arrangement's aforementioned packing efficiency of about 91%, the system's overall average surface reflectance is 91% of 55% or about 50%, implying a loss of about 50%. 41% of this loss is due to light absorption in circular non-reflective regions 82; the remaining 9% of this loss is due to light absorption in interstitial non-reflective gaps 84. Display 10's reflectance can be increased by decreasing such absorptive losses through the use of materials having specific selected refractive index values, optical microstructures or patterned surfaces placed on the outward or inward side(s) of monolayer 18 (FIG. 1A).
For example, since display 10's maximum surface reflectance is determined by the ratio of the refractive index values of hemi-bead 60 and electrophoretic medium 20, the reflectance can be increased by substituting air (refractive index=1.0) as electrophoretic medium 20 instead of a low refractive index liquid (refractive index less than 1.35).
Display 10's surface reflectance can be increased, as described below, without using particles suspended in an electrophoretic medium.
The foregoing examples of the related art and limitations related thereto are intended to be illustrative and not exclusive. Other limitations of the related art will become apparent to those of skill in the art upon a reading of the specification and a study of the drawings.